The role of görtler vortices in the hypersonic boundary layer transition

The Görtler vortices which manifest as the counter-rotating streamwise vortices in highspeed boundary layers are studied. Four groups of Ma numbers (Ma = 1.5, 3.0, 4.5 and 6.0) and three groups of wavenumbers (B = 0.5, 1.0 and 2.0×10^-3) are specified to investigate the parametric effect of Ma numbers and the spanwise wavenumbers on the spatial development and the interrelated secondary instability of Görtler vortices. The Görtler vortices in moderate supersonic flows (Ma=1.5, 3.0) are governed by the conventional wall-layer mode (mode W). In hypersonic flows (Ma=4.5, 6.0), it is the trapped-layer mode (mode T) that becomes dominating. The linear and nonlinear development of Görtler vortices are studied using the LST and the direct marching of the nonlinear parabolic equations. The secondary instabilities of Görtler vortices are then analyzed on the saturated state of the Görtler vortices with Floquet theory. The conclusion that "the dominating secondary modes (odd or even) depend on the spanwise wavenumbers of the Görtler vortices¹" is shown to be unapplicable in compressible cases. The relationship between the primary Görtler instability and the corresponding secondary instability are clarified. In the Görtler-dominated transition process, the most dangerous wavelength of the primary Görtler instability give rise to the largest growth rate of the secondary instability. The role of the Görtler vortices on the blunt compression/flared cone² is shown to be minor compared with the Mack mode. For the blunt compression wedge, it is the Görtler mode that becomes responsible for the flow transition as the Mack mode is considerably suppressed.